1. I'm not 100% sure, but I believe the mydlink site simply establishes a direct connection between the DCS-932L and client. So, if the client is on the LAN, the data stream should be confined to your LAN. Remote access, however, will clearly require a data stream from your LAN to the client elsewhere on the Internet.
2. The size of the data stream will vary greatly depending on whether the video is in Day Mode versus Night Mode. Night mode is a black and white stream, which will consume significantly less bandwidth than a comparable color video stream.
3. As the previous poster stated, the video stream is not secure.